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Effective Field Theory Methods to Model Compact Binaries

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Handbook of Gravitational Wave Astronomy

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Abstract

The gravitational two-body problem is currently subject of intense investigations, under compelling phenomenological and theoretical motivations. The gravitational wave detections from compact binary coalescences will demand even more accurate description of the source dynamics as the sensitivity of detectors increases over years. The analytic modeling of classical gravitational dynamics has been enriched over the last decade of powerful methods borrowed from field theory originally developed to describe fundamental particle quantum scatterings.

This work aims at presenting a review of a specific effort, initiated by the seminal paper by Goldberger and Rothstein, dubbed nonrelativistic general relativity, which applies effective field theory methods to describe the two-body dynamics in general relativity. It models the classical interaction between astrophysically massive objects via field theory methods, showing that many features usually associated with quantum field theory, e.g., divergences and counter-terms, renormalization group, loop expansions, and Feynman diagrams, have all to do with field theory, be it quantum or classical.

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References

  1. Aasi J et al (2015) Advanced LIGO. Class Quant Grav 32:074001. https://doi.org/10.1088/0264-9381/32/7/074001, 1411.4547

  2. Abbott B et al (2019) GWTC-1: a gravitational-wave transient catalog of compact binary mergers observed by LIGO and virgo during the first and second observing runs. Phys Rev X 9(3):031040. https://doi.org/10.1103/PhysRevX.9.031040, 1811.12907

  3. Abbott B et al (2020) GW190425: observation of a compact binary coalescence with total mass ∼ 3.4M⊙. Astrophys J Lett 892:L3. https://doi.org/10.3847/2041-8213/ab75f5, 2001.01761

  4. Abbott R et al (2020) GW190412: observation of a binary-black-hole coalescence with asymmetric masses. Phys Rev D 102(4):043015. https://doi.org/10.1103/PhysRevD.102.043015, 2004.08342

  5. Abbott R et al (2020) GW190521: a binary black hole merger with a total mass of 150 M⊙. Phys Rev Lett 125:101102. https://doi.org/10.1103/PhysRevLett.125.101102, 2009.01075

  6. Abbott R et al (2020) GW190814: gravitational waves from the coalescence of a 23 solar mass black hole with a 2.6 solar mass compact object. Astrophys J 896(2):L44. https://doi.org/10.3847/2041-8213/ab960f, 2006.12611

  7. Acernese F et al (2015) Advanced virgo: a second-generation interferometric gravitational wave detector. Class Quant Grav 32(2):024001. https://doi.org/10.1088/0264-9381/32/2/024001, 1408.3978

  8. Allen B, Anderson WG, Brady PR, Brown DA, Creighton JDE (2012) FINDCHIRP: an algorithm for detection of gravitational waves from inspiraling compact binaries. Phys Rev D85:122006. https://doi.org/10.1103/PhysRevD.85.122006, gr-qc/0509116

  9. Almeida GL, Foffa S, Sturani R (2020) Classical Gravitational Self-Energy from Double Copy 2008.06195

    Google Scholar 

  10. Barack L, Pound A (2019) Self-force and radiation reaction in general relativity. Rept Prog Phys 82(1):016904. https://doi.org/10.1088/1361-6633/aae552, 1805.10385

  11. Bern Z, Carrasco JJM, Johansson H (2008) New relations for Gauge-Theory Amplitudes. Phys Rev D78:085011. https://doi.org/10.1103/PhysRevD.78.085011, 0805.3993

  12. Bern Z, Cheung C, Roiban R, Shen CH, Solon MP, Zeng M (2019) Black hole binary dynamics from the double copy and effective theory. JHEP 10:206. https://doi.org/10.1007/JHEP10(2019)206, 1908.01493

  13. Bern Z, Cheung C, Roiban R, Shen CH, Solon MP, Zeng M (2019) Scattering amplitudes and the conservative hamiltonian for binary systems at third Post-Minkowskian Order. Phys Rev Lett 122(20):201603. https://doi.org/10.1103/PhysRevLett.122.201603, 1901.04424

  14. Bern Z, Luna A, Roiban R, Shen CH, Zeng M (2020) Spinning black hole binary dynamics, scattering amplitudes and effective field theory 2005.03071

    Google Scholar 

  15. Bernard L, Blanchet L, Faye G, Marchand T (2018) Center-of-mass equations of motion and conserved integrals of compact binary systems at the fourth Post-Newtonian Order. Phys Rev D 97(4):044037. https://doi.org/10.1103/PhysRevD.97.044037, 1711.00283

  16. Bini D, Damour T, Geralico A (2020) Sixth post-Newtonian nonlocal-in-time dynamics of binary systems 2007.11239

    Google Scholar 

  17. Binnington T, Poisson E (2009) Relativistic theory of tidal Love numbers. Phys Rev D 80:084018. https://doi.org/10.1103/PhysRevD.80.084018, 0906.1366

  18. Bjerrum-Bohr NJ, Damgaard PH, Festuccia G, Planté L, Vanhove P (2018) General relativity from scattering amplitudes. Phys Rev Lett 121(17):171601. https://doi.org/10.1103/PhysRevLett.121.171601, 1806.04920

  19. Blanchet L (2014) Gravitational radiation from post-newtonian sources and inspiralling compact binaries. Living Rev Rel 17:2. https://doi.org/10.12942/lrr-2014-2, 1310.1528

  20. Blanchet L, Damour T (1988) Tail transported temporal correlations in the dynamics of a gravitating system. Phys Rev D 37:1410. https://doi.org/10.1103/PhysRevD.37.1410

    Article  ADS  Google Scholar 

  21. Blanchet L, Foffa S, Larrouturou F, Sturani R (2020) Logarithmic tail contributions to the energy function of circular compact binaries. Phys Rev D 101(8):084045. https://doi.org/10.1103/PhysRevD.101.084045, 1912.12359

  22. Blümlein J, Maier A, Marquard P (2019) The gravitational potential of two point masses at five loops. PoS RADCOR2019:029. https://doi.org/10.22323/1.375.0029, 1912.03089

  23. Blümlein J, Maier A, Marquard P (2020) Five-loop static contribution to the gravitational interaction potential of two point masses. Phys Lett B 800:135100. https://doi.org/10.1016/j.physletb.2019.135100, 1902.11180

  24. Blümlein J, Maier A, Marquard P, Schäfer G (2020) Testing binary dynamics in gravity at the sixth post-Newtonian level. Phys Lett B 807:135496. https://doi.org/10.1016/j.physletb.2020.135496, 2003.07145

  25. Boyle M et al (2019) The SXS collaboration catalog of binary black hole simulations. Class Quant Grav 36(19):195006. https://doi.org/10.1088/1361-6382/ab34e2, 1904.04831

  26. Chetyrkin KG, Tkachov FV (1981) Integration by parts: the algorithm to calculate beta functions in 4 loops. Nucl Phys B192:159–204. https://doi.org/10.1016/0550-3213(81)90199-1

  27. Damour T (1984) The motion of compact bodies and gravitational radiation. Springer Netherlands, Dordrecht, pp 89–106. https://doi.org/10.1007/978-94-009-6469-3_7

    Google Scholar 

  28. Damour T (2020) Classical and quantum scattering in post-Minkowskian gravity. Phys Rev D 102(2):024060. https://doi.org/10.1103/PhysRevD.102.024060, 1912.02139

  29. Damour T, Lecian OM (2009) On the gravitational polarizability of black holes. Phys Rev D 80:044017. https://doi.org/10.1103/PhysRevD.80.044017, 0906.3003

  30. Detweiler SL, Brown J, Lee H (1997) The PostMinkowski expansion of general relativity. Phys Rev D 56:826–841. https://doi.org/10.1103/PhysRevD.56.826, gr-qc/9609010

  31. Donoghue JF (1994) General relativity as an effective field theory: the leading quantum corrections. Phys Rev D 50:3874–3888. https://doi.org/10.1103/PhysRevD.50.3874, gr-qc/9405057

  32. Foffa S, Sturani R (2013) Dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant. Phys Rev D 87(6):064011. https://doi.org/10.1103/PhysRevD.87.064011, 1206.7087

  33. Foffa S, Sturani R (2013) Tail terms in gravitational radiation reaction via effective field theory. Phys Rev D87(4):044056. https://doi.org/10.1103/PhysRevD.87.044056, 1111.5488

  34. Foffa S, Sturani R (2014) Effective field theory methods to model compact binaries. Class Quant Grav 31(4):043001. https://doi.org/10.1088/0264-9381/31/4/043001, 1309.3474

  35. Foffa S, Sturani R (2019) Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: regularized lagrangian. Phys Rev D 100(2):024047. https://doi.org/10.1103/PhysRevD.100.024047, 1903.05113

  36. Foffa S, Sturani R (2020) Hereditary terms at next-to-leading order in two-body gravitational dynamics. Phys Rev D 101(6):064033. https://doi.org/10.1103/PhysRevD.101.064033, 1907.02869

  37. Foffa S, Mastrolia P, Sturani R, Sturm C (2017) Effective field theory approach to the gravitational two-body dynamics, at fourth post-Newtonian order and quintic in the Newton constant. Phys Rev D 95(10):104009. https://doi.org/10.1103/PhysRevD.95.104009, 1612.00482

  38. Foffa S, Mastrolia P, Sturani R, Sturm C, Torres Bobadilla WJ (2019) Calculating the static gravitational two-body potential to fifth post-Newtonian order with Feynman diagrams. PoS RADCOR2019:027. https://doi.org/10.22323/1.375.0027, 1912.04720

  39. Foffa S, Mastrolia P, Sturani R, Sturm C, Torres Bobadilla WJ (2019) Static two-body potential at fifth post-Newtonian order. Phys Rev Lett 122(24):241605. https://doi.org/10.1103/PhysRevLett.122.241605, 1902.10571

  40. Foffa S, Porto RA, Rothstein I, Sturani R (2019) Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian. Phys Rev D100(2):024048. https://doi.org/10.1103/PhysRevD.100.024048, 1903.05118

  41. Friedman JL, Uryu K, Shibata M (2002) Thermodynamics of binary black holes and neutron stars. Phys Rev D 65:064035. https://doi.org/10.1103/PhysRevD.70.129904, [Erratum: Phys.Rev.D 70, 129904 (2004)], gr-qc/0108070

  42. Galley CR (2013) Classical mechanics of nonconservative systems. Phys Rev Lett 110(17):174301. https://doi.org/10.1103/PhysRevLett.110.174301, 1210.2745

  43. Galley CR, Tiglio M (2009) Radiation reaction and gravitational waves in the effective field theory approach. Phys Rev D 79:124027. https://doi.org/10.1103/PhysRevD.79.124027, 0903.1122

  44. Galley CR, Leibovich AK, Porto RA, Ross A (2016) Tail effect in gravitational radiation reaction: time nonlocality and renormalization group evolution. Phys Rev D 93:124010. https://doi.org/10.1103/PhysRevD.93.124010, 1511.07379

  45. Goldberger WD (2007) Les Houches lectures on effective field theories and gravitational radiation. In: Les Houches summer school – session 86: particle physics and cosmology: the fabric of spacetime, hep-ph/0701129

    Google Scholar 

  46. Goldberger WD, Ridgway AK (2017) Radiation and the classical double copy for color charges. Phys Rev D 95(12):125010. https://doi.org/10.1103/PhysRevD.95.125010, 1611.03493

  47. Goldberger WD, Ridgway AK (2018) Bound states and the classical double copy. Phys Rev D 97(8):085019. https://doi.org/10.1103/PhysRevD.97.085019, 1711.09493

  48. Goldberger WD, Ross A (2010) Gravitational radiative corrections from effective field theory. Phys Rev D 81:124015. https://doi.org/10.1103/PhysRevD.81.124015, 0912.4254

  49. Goldberger WD, Rothstein IZ (2006) An effective field theory of gravity for extended objects. Phys Rev D 73:104029. https://doi.org/10.1103/PhysRevD.73.104029, hep-th/0409156

  50. Goldberger WD, Rothstein IZ (2020) Horizon radiation reaction forces 2007.00731

    Google Scholar 

  51. Goldberger WD, Ross A, Rothstein IZ (2014) Black hole mass dynamics and renormalization group evolution. Phys Rev D 89(12):124033. https://doi.org/10.1103/PhysRevD.89.124033, 1211.6095

  52. Jantzen B (2011) Foundation and generalization of the expansion by regions. JHEP 12:076. https://doi.org/10.1007/JHEP12(2011)076, 1111.2589

  53. Jordan R (1986) Effective field equations for expectation values. Phys Rev D 33:444–454. https://doi.org/10.1103/PhysRevD.33.444

    Article  MathSciNet  ADS  Google Scholar 

  54. Kälin G, Porto RA (2020) From boundary data to bound states. JHEP 01:072. https://doi.org/10.1007/JHEP01(2020)072, 1910.03008

  55. Kälin G, Porto RA (2020) Post-Minkowskian effective field theory for conservative binary dynamics 2006.01184

    Google Scholar 

  56. Kälin G, Liu Z, Porto RA (2020) Conservative dynamics of binary systems to third Post-Minkowskian order from the effective field theory approach 2007.04977

    Google Scholar 

  57. Kavanagh C, Ottewill AC, Wardell B (2015) Analytical high-order post-Newtonian expansions for extreme mass ratio binaries. Phys Rev D 92(8):084025. https://doi.org/10.1103/PhysRevD.92.084025, 1503.02334

  58. Khan S, Ohme F, Chatziioannou K, Hannam M (2020) Including higher order multipoles in gravitational-wave models for precessing binary black holes. Phys Rev D 101(2):024056. https://doi.org/10.1103/PhysRevD.101.024056, 1911.06050

  59. Kol B, Smolkin M (2008) Non-relativistic gravitation: from Newton to Einstein and back. Class Quant Grav 25:145011. https://doi.org/10.1088/0264-9381/25/14/145011, 0712.4116

  60. Kol B, Smolkin M (2012) Black hole stereotyping: induced gravito-static polarization. JHEP 02:010. https://doi.org/10.1007/JHEP02(2012)010, 1110.3764

  61. Laarakkers WG, Poisson E (1999) Quadrupole moments of rotating neutron stars. Astrophys J 512:282–287. https://doi.org/10.1086/306732, gr-qc/9709033

  62. Le Tiec A, Blanchet L, Whiting BF (2012) The first law of binary black hole mechanics in general relativity and Post-Newtonian theory. Phys Rev D 85:064039. https://doi.org/10.1103/PhysRevD.85.064039, 1111.5378

  63. Leibovich AK, Maia NT, Rothstein IZ, Yang Z (2020) Second post-Newtonian order radiative dynamics of inspiralling compact binaries in the Effective Field Theory approach. Phys Rev D 101(8):084058. https://doi.org/10.1103/PhysRevD.101.084058, 1912.12546

  64. Levi M (2020) Effective field theories of post-newtonian gravity: a comprehensive review. Rept Prog Phys 83(7):075901. https://doi.org/10.1088/1361-6633/ab12bc, 1807.01699

  65. Levi M, Teng F (2020) NLO gravitational quartic-in-spin interaction 2008.12280

    Google Scholar 

  66. Levi M, Mougiakakos S, Vieira M (2019) Gravitational cubic-in-spin interaction at the next-to-leading post-Newtonian order 1912.06276

    Google Scholar 

  67. Levi M, Mcleod AJ, Von Hippel M (2020) N3LO gravitational spin-orbit coupling at order G4 2003.02827

    Google Scholar 

  68. Levi M, Mcleod AJ, Von Hippel M (2020) NNNLO gravitational quadratic-in-spin interactions at the quartic order in G 2003.07890

    Google Scholar 

  69. Li J, Prabhu SG (2018) Gravitational radiation from the classical spinning double copy. Phys Rev D 97(10):105019. https://doi.org/10.1103/PhysRevD.97.105019, 1803.02405

  70. Maggiore M (2005) A modern introduction to quantum field theory. EBSCO ebook academic collection, Oxford University Press. https://books.google.com.br/books?id=yykTDAAAQBAJ

    MATH  Google Scholar 

  71. Manohar AV, Stewart IW (2007) The zero-bin and mode factorization in quantum field theory. Phys Rev D 76:074002. https://doi.org/10.1103/PhysRevD.76.074002, hep-ph/0605001

  72. Ossokine S et al (2020) Multipolar effective-one-body waveforms for precessing binary black holes: construction and validation. Phys Rev D 102(4):044055. https://doi.org/10.1103/PhysRevD.102.044055, 2004.09442

  73. Pani P, Gualtieri L, Ferrari V (2015) Tidal Love numbers of a slowly spinning neutron star. Phys Rev D 92(12):124003. https://doi.org/10.1103/PhysRevD.92.124003, 1509.02171

  74. Pardo BA, Maia NT (2020) Next-to-leading order spin-orbit effects in the equations of motion, energy loss and phase evolution of binaries of compact bodies in the effective field theory approach 2009.05628

    Google Scholar 

  75. Poisson E (1998) Gravitational waves from inspiraling compact binaries: the quadrupole moment term. Phys Rev D 57:5287–5290. https://doi.org/10.1103/PhysRevD.57.5287, gr-qc/9709032

  76. Poisson E (2004) Absorption of mass and angular momentum by a black hole: Time-domain formalisms for gravitational perturbations, and the small-hole / slow-motion approximation. Phys Rev D 70:084044. https://doi.org/10.1103/PhysRevD.70.084044, gr-qc/0407050

  77. Poisson E (2015) Tidal deformation of a slowly rotating black hole. Phys Rev D 91(4):044004. https://doi.org/10.1103/PhysRevD.91.044004, 1411.4711

  78. Porto RA (2006) Post-Newtonian corrections to the motion of spinning bodies in NRGR. Phys Rev D 73:104031. https://doi.org/10.1103/PhysRevD.73.104031, gr-qc/0511061

  79. Porto RA (2008) Absorption effects due to spin in the worldline approach to black hole dynamics. Phys Rev D 77:064026. https://doi.org/10.1103/PhysRevD.77.064026, 0710.5150

  80. Porto RA (2016) The effective field theorist’s approach to gravitational dynamics. Phys Rept 633:1–104. https://doi.org/10.1016/j.physrep.2016.04.003, 1601.04914

  81. Porto RA, Rothstein IZ (2017) Apparent ambiguities in the post-Newtonian expansion for binary systems. Phys Rev D 96(2):024062. https://doi.org/10.1103/PhysRevD.96.024062, 1703.06433

  82. Porto RA, Ross A, Rothstein IZ (2011) Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order. JCAP 03:009. https://doi.org/10.1088/1475-7516/2011/03/009, 1007.1312

  83. Porto RA, Ross A, Rothstein IZ (2012) Spin induced multipole moments for the gravitational wave amplitude from binary inspirals to 2.5 Post-Newtonian order. JCAP 09:028. https://doi.org/10.1088/1475-7516/2012/09/028, 1203.2962

  84. Studerus C (2010) Reduze-Feynman integral reduction in C++. Comput Phys Commun 181:1293–1300. https://doi.org/10.1016/j.cpc.2010.03.012, 0912.2546

  85. ’t Hooft G, Veltman M (1972) Regularization and renormalization of gauge fields. Nuclear Physics B 44(1):189–213. https://doi.org/10.1016/0550-3213(72)90279-9

  86. Thorne KS (1980) Multipole expansions of gravitational radiation. Rev Mod Phys 52:299–339. https://doi.org/10.1103/RevModPhys.52.299

    Article  MathSciNet  ADS  Google Scholar 

  87. Tkachov FV (1981) A theorem on analytical calculability of four loop renormalization group functions. Phys Lett B100:65–68. https://doi.org/10.1016/0370-2693(81)90288-4

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Acknowledgements

This work has been partially supported by CNPq. The author wishes to thank Stefano Foffa for long-lasting collaboration and discussions. The author would like to thank ICTP-SAIFR FAPESP grant 2016/01343-7.

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Authors and Affiliations

  1. International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal, Brazil

    Riccardo Sturani

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  1. Riccardo Sturani
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Correspondence to Riccardo Sturani .

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Editors and Affiliations

  1. Department of Physics, Fudan University, Shanghai, China

    Cosimo Bambi

  2. Université de Paris and European Gravitational Observatory, Paris, France

    Stavros Katsanevas

  3. Institute for Astronomy and Astrophysics Eberhard Karls, University of Tübingen, Tübingen, Germany

    Konstantinos D. Kokkotas

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Sturani, R. (2022). Effective Field Theory Methods to Model Compact Binaries. In: Bambi, C., Katsanevas, S., Kokkotas, K.D. (eds) Handbook of Gravitational Wave Astronomy. Springer, Singapore. https://doi.org/10.1007/978-981-16-4306-4_32

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